journal6 ›› 2003, Vol. 24 ›› Issue (4): 1-2.

• Mathematics •     Next Articles

On the Diophantine Equation xp+2mp=pDy2


  1. (Department of Mathematics,Zhanjiang Normal College,Zhanjiang 524048,Guangdong China)
  • Online:2003-12-15 Published:2012-11-06

Abstract: Let p be an odd prime,m be a positive integer,D be a positive integer with square free.In this paper the author proves that if p>3,m>1 and D is not divisible by p or primes of the form 2kp+1,then the equation xp+2mp=pDy2 has no positive integer solutions (x,y) with gcd (x,y)=1.

Key words: higher diophantine equation, positive integer solution, existence

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